The Stacks project

Definition 13.9.4. Let $\mathcal{A}$ be an additive category. A termwise split injection $\alpha : A^\bullet \to B^\bullet $ is a morphism of complexes such that each $A^ n \to B^ n$ is isomorphic to the inclusion of a direct summand. A termwise split surjection $\beta : B^\bullet \to C^\bullet $ is a morphism of complexes such that each $B^ n \to C^ n$ is isomorphic to the projection onto a direct summand.

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